Determine the degree of each of the following polynomials- i 4x-5x2-6x3-2x ii y2y-y3 iii 3x-22x3-3x2 iv -1-2x-3 v -8 vi x2x4-x2

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Degree of a Polynomial

Determine the...

Question

Determine the degree of each of the following polynomials.

(i) $\frac{4 x - 5 x^{2} + 6 x^{3}}{2 x}$

(ii) $y^{2} (y - y^{3})$

(iii) $(3 x - 2) (2 x^{3} + 3 x^{2})$

(iv) $- \frac{1}{2} x + 3$

(v) $- 8$

(vi) $x^{2} (x^{4} + x^{2})$

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Solution

(i) $\frac{4 x - 5 x^{2} + 6 x^{3}}{2 x}$
Here, the highest power of x is 2. So, the degree of the polynomial is 2.

(ii) $y^{2} (y - y^{3})$
Here, the highest power of y is 5. So, the degree of the polynomial is 5.

(iii) $(3 x - 2) (2 x^{3} + 3 x^{2}) = 6 x^{4} + 9 x^{3} - 4 x^{3} - 6 x^{2} = 6 x^{4} + 5 x^{3} - 6 x^{2}$
Here, the highest power of x is 4. So, the degree of the polynomial is 4.

(iv) $- \frac{1}{2} x + 3$
Here, the highest power of x is 1. So, the degree of the polynomial is 1.

(v) $- 8$
–8 is a constant polynomial. So, the degree of the polynomial is 0.

(vi) $(x - 2) (x^{4} + x^{2}) = x^{2} + x^{0} = x^{2} + 1$
Here, the highest power of x is 2. So, the degree of the polynomial is 2.

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Similar questions

Q. Write the degree of each of the following polynomials.
(i) 2x² + 5x² − 7
(ii) 5x² − 3x + 2
(iii) 2x + x² − 8
(iv)

\frac{1}{2} y^{7} - 12 y^{6} + 48 y^{5} - 10

(v) 3x³ + 1
(vi) 5
(vii) 20x³ + 12x²y² − 10y² + 20

Q. Determine the degree of the the polynomial.

(3 x - 2) (2 x^{3} + 3 x^{2})

Write the degree of each polynomial given below:

(i) $x y + 7 z$ (ii) $x^{2} - 6 x^{3} + 8$

(iii) $y - 6 y^{2} + 5 y^{8}$ (iv) $x y z - 3$

(v) $x y + y z^{2} - z x^{3}$ (vi) $x^{5} y^{7} - 8 x^{3} y^{8} + 10 x^{4} y^{4} z^{4}$

Question 2
Determine the degree of each of the following polynomials.
(i) $2 x - 1$

(ii) $- 10$

(iii) $x^{3} - 9 x + 3 x^{5}$

(iv) $y^{3} (1 - y^{4})$

Q. Rewrite each of the following polynomials in standard form.
(i)

x - 2 x^{2} + 8 + 5 x^{3}

(ii)

\frac{2}{3} + 4 y^{2} - 3 y + 2 y^{3}

(iii)

6 x^{3} + 2 x - x^{5} - 3 x^{2}

(iv)

2 + t - 3 t^{3} + t^{4} - t^{2}

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Determine the degree of each of the following polynomials. (i) 4x−5x2+6x32x (ii) y2(y−y3) (iii) (3x−2)(2x3+3x2) (iv) −12x+3 (v) −8 (vi) x2(x4+x2)

Determine the degree of each of the following polynomials.

(i) $\frac{4 x - 5 x^{2} + 6 x^{3}}{2 x}$

(ii) $y^{2} (y - y^{3})$

(iii) $(3 x - 2) (2 x^{3} + 3 x^{2})$

(iv) $- \frac{1}{2} x + 3$

(v) $- 8$

(vi) $x^{2} (x^{4} + x^{2})$